New fermions in the bulk

Spinor fields on 5-dimensional Lorentzian manifolds are classified, according to the geometric Fierz identities that involve their bilinear covariants. Based upon this classification that generalises the celebrated 4-dimensional Lounesto classification of spinor fields, new non-trivial classes of 5-dimensional spinor fields are, hence, found, with important potential applications regarding bulk fermions and their subsequent localisation on brane-worlds. In addition, quaternionic bilinear covariants are used to derive the quaternionic spin density, through the truncated exterior bundle. In order to accomplish a realisation of these new spinors, a Killing vector field is constructed on the horizon of 5-dimensional Kerr black holes. This Killing vector field is shown to reach the time-like Killing vector field at the spatial infinity, through a current 1-form density, constructed with the derived new spinor fields. The current density is, moreover, expressed as the f\"unfbein components, assuming a condensed form.